6k^2+32k+64=0

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Solution for 6k^2+32k+64=0 equation: 


Simplifying
6k2 + 32k + 64 = 0

Reorder the terms:
64 + 32k + 6k2 = 0

Solving
64 + 32k + 6k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '2'.
2(32 + 16k + 3k2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(32 + 16k + 3k2)' equal to zero and attempt to solve:

Simplifying
32 + 16k + 3k2 = 0

Solving
32 + 16k + 3k2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
10.66666667 + 5.333333333k + k2 = 0

Move the constant term to the right:

Add '-10.66666667' to each side of the equation.
10.66666667 + 5.333333333k + -10.66666667 + k2 = 0 + -10.66666667

Reorder the terms:
10.66666667 + -10.66666667 + 5.333333333k + k2 = 0 + -10.66666667

Combine like terms: 10.66666667 + -10.66666667 = 0.00000000
0.00000000 + 5.333333333k + k2 = 0 + -10.66666667
5.333333333k + k2 = 0 + -10.66666667

Combine like terms: 0 + -10.66666667 = -10.66666667
5.333333333k + k2 = -10.66666667

The k term is 5.333333333k.  Take half its coefficient (2.666666667).
Square it (7.111111113) and add it to both sides.

Add '7.111111113' to each side of the equation.
5.333333333k + 7.111111113 + k2 = -10.66666667 + 7.111111113

Reorder the terms:
7.111111113 + 5.333333333k + k2 = -10.66666667 + 7.111111113

Combine like terms: -10.66666667 + 7.111111113 = -3.555555557
7.111111113 + 5.333333333k + k2 = -3.555555557

Factor a perfect square on the left side:
(k + 2.666666667)(k + 2.666666667) = -3.555555557

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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